Yet another Twin Paradox thread

[Mike_Fontenot]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

It's the usual problem of what is meant by "sees" ... that term gets used with different meanings, by different people, in special relativity.

The image currently being SEEN by an approaching ship IS smaller than the image currently being SEEN by a stationary ship at that same location. But the approaching ship is seeing the Earth NOT as it currently IS, but as it WAS at an earlier time, when it was farther away. When those on the approaching ship correct for that delay in the propagation of light, they will conclude that the Earth is closer than what those on the stationary ship conclude.

Mike Fontenot

 

[Buckethead]

It's the usual problem of what is meant by "sees" ... that term gets used with different meanings, by different people, in special relativity.

The image currently being SEEN by an approaching ship IS smaller than the image currently being SEEN by a stationary ship at that same location. But the approaching ship is seeing the Earth NOT as it currently IS, but as it WAS at an earlier time, when it was farther away. When those on the approaching ship correct for that delay in the propagation of light, they will conclude that the Earth is closer than what those on the stationary ship conclude.

Mike Fontenot

But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth. And this of course will be what they both hear since they are in the same location. So it may appear smaller (as I said earlier, because its an illusion) and it can also appear to be closer because their time has slowed down and they will reach Earth in less time than they thought, but both of these are an illusion because in fact the moving ship and the stationary ship and the departing ship are all the same distance from the Earth as indicated from the encoded message from Earth. So it appears I am still missing something.

 

[michelcolman]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

When you are traveling towards or away from the earth, the Earth will "be" closer to you than if you would be standing still at exactly the same location. You could measure this distance by multiplying your travel time with your speed, so it's a "real" distance. Also, experiments sending a laser beam back and forth would be perfectly consistent with this distance. Of course people on Earth would not agree, and neither would people at the same location as you but that are not moving relative to earth. For you, however, this shorter distance will be perfectly real.

The visual effect, however, is a bit different.

If you are moving towards the earth, its physical size will appear smaller because your field of view widens. Basically, you are receiving the same light as a stationary observer, but the rays seem to come from smaller angles. In fact, if you go fast enough, you will even see objects that are at an angle behind you but that appear to be in front of you! So, when accellerating to really high speeds, you will get the visual impression that you are going backwards. Everything in front of you will also become brighter and blueshifted.

When moving in the opposite direction, away from Earth and looking backwards, the Earth will look bigger but fainter and redshifted. While accellerating, the objects behind you (that you are accellerating away from) will actually appear to be coming closer to you. So in this case too, the accelleration will create the illusion of going backwards.

You can see these effects in action on:
http://www.anu.edu.au/Physics/Searle/

 

[michelcolman]

But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth. And this of course will be what they both hear since they are in the same location. So it may appear smaller (as I said earlier, because its an illusion) and it can also appear to be closer because their time has slowed down and they will reach Earth in less time than they thought, but both of these are an illusion because in fact the moving ship and the stationary ship and the departing ship are all the same distance from the Earth as indicated from the encoded message from Earth. So it appears I am still missing something.

What's missing is how long it took for the message to reach you. One person may say that Earth's message was sent an hour ago, while the other will say that the same message was sent two hours ago. That means they will disagree on the current time on earth, and the current distance from earth.

If you are moving away from earth, you will say that the Earth is moving away from you and therefore it is now further away from you than it was when the message was sent. Somebody receiving the same message but going towards earth, will say that the Earth is coming towards him and therefore it is now closer than it was when the message was sent. That also means current time at Earth is now later, since the message had to travel a longer distance so it must have been sent longer ago. Both will be right, from their point of view! The speed of light relative to themselves is indisputably c, and therefore their conclusions are the only possible explanation.

 

[Buckethead]

When you are traveling towards or away from the earth, the Earth will "be" closer to you than if you would be standing still at exactly the same location. You could measure this distance by multiplying your travel time with your speed, so it's a "real" distance. Also, experiments sending a laser beam back and forth would be perfectly consistent with this distance. Of course people on Earth would not agree, and neither would people at the same location as you but that are not moving relative to earth. For you, however, this shorter distance will be perfectly real.

The visual effect, however, is a bit different.

If you are moving towards the earth, its physical size will appear smaller because your field of view widens. Basically, you are receiving the same light as a stationary observer, but the rays seem to come from smaller angles. In fact, if you go fast enough, you will even see objects that are at an angle behind you but that appear to be in front of you! So, when accellerating to really high speeds, you will get the visual impression that you are going backwards. Everything in front of you will also become brighter and blueshifted.

When moving in the opposite direction, away from Earth and looking backwards, the Earth will look bigger but fainter and redshifted. While accellerating, the objects behind you (that you are accellerating away from) will actually appear to be coming closer to you. So in this case too, the accelleration will create the illusion of going backwards.

You can see these effects in action on:
http://www.anu.edu.au/Physics/Searle/

Thank you, this is what I thought which is why in a much earlier post I said that the Earth only looks further away, an illusion. And yes I can see how it will "actually" be closer because of the slowing of time for the returning traveller. These are all consistant with my understanding.

Somehow though, this still feels circular to me because you are saying the Earth is closer upon returning because all measurements indicate that it is closer (which is fine). But of course it is not closer than the departing ship when they are in the same location because of the encoded time message which is the same for both.

So far I am just seeing that everything is just an illusion except for the slowed time when the ship returns to Earth. The departing ship sees the Earth aging more slowly , but this is an illusion, the two ships see different distances to Earth and this is also an illusion, and the returning ship sees the Earth clock moving more slowly which is also an illusion, so the only thing that is not an illusion is the clock on the two ships is going slower than the clock on Earth. I don't think I'll ever understand this.

 

[Mike_Fontenot]

[...]
But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth.
[...]

No, that's not correct. They DO each hear EXACTLY the same message, but when they each CORRECTLY allow for the transit time of that message, they get DIFFERENT answers. They are BOTH correct.

And there are easier ways for them to determine their current distance from the earth.

They can use the Lorentz equations.

They can use the length-contraction result.

They can use the time-dilation result, combined with their known velocity with respect to the earth.

All four methods yield exactly the same result.

Mike Fontenot

 

[Buckethead]

What's missing is how long it took for the message to reach you. One person may say that Earth's message was sent an hour ago, while the other will say that the same message was sent two hours ago. That means they will disagree on the current time on earth, and the current distance from earth.

If you are moving away from earth, you will say that the Earth is moving away from you and therefore it is now further away from you than it was when the message was sent. Somebody receiving the same message but going towards earth, will say that the Earth is coming towards him and therefore it is now closer than it was when the message was sent. That also means current time at Earth is now later, since the message had to travel a longer distance so it must have been sent longer ago. Both will be right, from their point of view! The speed of light relative to themselves is indisputably c, and therefore their conclusions are the only possible explanation.

OK, yes I can see this, but I think it's fair to say that when one ship says it was sent a different time than the other, they are simply using their instruments and calculators to say that and that in fact the message had to have been sent at the same time (it's only one message) and had to have been received at the same time (they are both there to receive it), and the message says the same time to both of them, so the only conclusion to be made from this is that THIS is the actual distance from Earth and it's one and the same distance for both ships. What I understand can't be determined is the actual distance in units as both ships will come up with a different number. So both numbers must be wrong since the two numbers MUST agree with each other since they are in the same location.

 

[Buckethead]

No, that's not correct. They DO each hear EXACTLY the same message, but when they each CORRECTLY allow for the transit time of that message, they get DIFFERENT answers. They are BOTH correct.

And there are easier ways for them to determine their current distance from the earth.

They can use the Lorentz equations.

They can use the length-contraction result.

They can use the time-dilation result, combined with their known velocity with respect to the earth.

All four methods yield exactly the same result.

Mike Fontenot

Agreed. But see post #67. You can't both be at different distances and at the same distance at the same time, this is a paradox

 

[Mike_Fontenot]

[...]
But see post #67. You can't both be at different distances and at the same distance at the same time, this is a paradox
[...]

They each agree how old the home twin was when she SENT the message ... her message tells them that.

And they each agree about how old THEY each were when they simultaneously RECEIVED her message.

But they disagree about how much the home twin aged during the message transit, and therefore they disagree about how old the home twin was when they RECEIVED her message.

There are no true paradoxes and/or inconsistencies in special relativity. But it is very easy to THINK you see an inconsistency, whenever you allow yourself to be even the slightest bit imprecise in your statements, or when you allow a subconsciousassumption to creep in, that is obviously true in Newtonian physics, but which is NOT true in special relativity. Everyone who has ever carried out any calculations in special relativity has been burned before (usually multiple times) because they haven't been sufficiently precise in their statements.

Mike Fontenot

 

[phyti]

They each agree how old the home twin was when she SENT the message ... her message tells them that.

And they each agree about how old THEY each were when they simultaneously RECEIVED her message.

But they disagree about how much the home twin aged during the message transit, and therefore they disagree about how old the home twin was when they RECEIVED her message.

There are no true paradoxes and/or inconsistencies in special relativity. But it is very easy to THINK you see an inconsistency, whenever you allow yourself to be even the slightest bit imprecise in your statements, or when you allow a subconsciousassumption to creep in, that is obviously true in Newtonian physics, but which is NOT true in special relativity. Everyone who has ever carried out any calculations in special relativity has been burned before (usually multiple times) because they haven't been sufficiently precise in their statements.

Mike Fontenot

But what if ships 1 and 2 do not synchronize their clocks upon leaving earth?
What would they conclude about the message?

 

[Mike_Fontenot]

But what if ships 1 and 2 do not synchronize their clocks upon leaving earth?
What would they conclude about the message?

Irrelevant to the above discussion.

 

[sylas]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

Yes, it does.

Specifically, consider a star that is six light years from Earth, as measured in a frame where the star and Earth are at rest. Consider Earth sending a radio message to the star. I'll locate events using (x,t) co-ordinates (distance and time) in different frames, but I will keep the event (0,0) to be the event of receiving the message at the distant star, with positive x in the direction of Earth. Units are years and lightyears, and so Earth is at rest at location x=6 in the star rest frame.

In the star rest frame, the event of Earth sending the message is (6,-6). It was six years ago.

In the rest frame of a ship moving past the star at 60% light speed, towards the Earth, the event of Earth sending the message is (12,-12). In the rest frame of a ship moving past the star away from the Earth at 60% light speed, the event is (3,-3).

These are not illusions. They are co-ordinates in different frames, with no frame standing out as correct. All distance and time measurements between events are always relative to some frame. There is no one correct value.

Cheers -- sylas

PS. Note that this is the distance between events; NOT the distance between Earth and the star. In the rest frame of the ship, Earth and the star are both moving at 60% light speed, and they are 4.8 light years apart from each other.

A radio message between Earth and the star takes 12 years one way and 3 years the other way because the speed of light is totally unaffected by the motions, and the light signal is chasing a moving receiver. In 3 years the receiver moving at 60% light speed moves 1.8 light years, and if this is reducing the distance light must travel from emission, then the distance to cover is 4.8 - 1.8 = 3 light years.

In 12 years the receiver moving at 60% light speed moves 7.2 light years. If this is increasing the distance light must travel from emission, then the distance to cover is 4.8 + 7.2 = 12 light years.

In the star rest frame, the receiver is not moving, and the distance from Earth to star is 6 light years.

 

[phyti]

Irrelevant to the above discussion.

Is that your final answer?

 

[phyti]

Yes, it does.
These are not illusions. .

Yes they are because of the simultaneity and synchronization definitions.
The absolute propagation speed c is sustituted for the relative (closing) speed of light.
1905 paper, par 1 & 2.

 

[sylas]

Yes they are because of the simultaneity and synchronization definitions.
The absolute propagation speed c is sustituted for the relative (closing) speed of light.
1905 paper, par 1 & 2.

You are being cryptic -- and not only in response to me. I'm not bothering with this unless YOU make the effort to give a clear exposition of what you mean.

A suitable translation into English of Einstein's famous paper On the Electrodynamics of Moving Bodies is available at the link. It does not have the word "illusion" in any paragraph; and the paragraphs you might be referring to do not back up your denial of what I posted and explained previously.

In the meantime, what I said is entirely correct. I am not speaking of illusions, but of genuine distance and time measures.

While we are at it. I agree entirely with Mike Fontenot that your post about not synchronizing clocks was irrelevant to the discussion; but whether a reply is "final" or not actually depends on YOU describing what you mean much better. If your "final" input on synchronization is given, then Mike's response is apt as a "final" response. If you want to keep talking, then the ball is in your court; not Mike's.

Sylas

 

[John232]

Say, two ships start raceing toward each other at a speed close to the speed of light. Each ship looks at the other ship and they both measure each others clocks going slower then their own. Then Earth looks at both ships, they both took off from an Earth station, and Earth measures both of their clocks to measure the same time that is slower than Earths clock. They both accelerated at the same rate to reach the same speed close to the speed of light.

What does each ship and Earth clock say to agree that they both read each others clock as being slower while Earth reads both their clocks as being the same slower speed?

The problem is that the 3 observers wouldn't be able to agree on anything the other clocks should read. They couldn't read a slower time and the same time at the same time. Each observer would have to see a different reading on the clock than the person traveling along with the clock. It would seem almost like there would have to be a separate reality for each observer to achieve what SR would say about the situtation.

 

[ghwellsjr]

The only problem is you have the two ships racing toward each other when I think you want them racing away from each other (and from the earth) but otherwise this is no different than the first half of the Twin Paradox.

Any two observers in relative motion will see the other one's clock as running slower than their own and by the same amount. You have three such pairs of observers. The two ships will measure more time dilation between them than either of them with the earth. Each earth-ship measurement will be the same assuming that both ships are traveling at the same speed but in opposite directions.

If you had both ships turn around at the same time and head back to earth, their times would end up identical but smaller than the time on the Earth clock.

 

[John232]

The only problem is you have the two ships racing toward each other when I think you want them racing away from each other (and from the earth) but otherwise this is no different than the first half of the Twin Paradox.

I don't see how direction of motion is a issue. But, yes it is just the first half of the Twin Paradox. Say, the ships went close enough to the speed of light they aged 3 times slower.

Three Earth secounds goes by, Earth reads each clock on each ship to only have read 1 secound. Each ship reads his clock to have read 3 secounds, and Earth and the other ship 1 secound. They all try to sync their clocks to read the same time. How is this possible if they all read different times on each others clocks?

 

[michelcolman]

I don't see how direction of motion is a issue. But, yes it is just the first half of the Twin Paradox. Say, the ships went close enough to the speed of light they aged 3 times slower.

Three Earth secounds goes by, Earth reads each clock on each ship to only have read 1 secound. Each ship reads his clock to have read 3 secounds, and Earth and the other ship 1 secound. They all try to sync their clocks to read the same time. How is this possible if they all read different times on each others clocks?

The answer to your problem is that it is impossible to sync their clocks unambiguously if they are not in the same location. Earth and the ships will not agree on the exact time at which the others "synced" their clocks, they will all say that the others pushed their triggers too early or too late. If Earth observes the two ships pressing their sync triggers simultaneously, each ship will say the other pressed it a lot earlier (if moving towards each other) or later (if moving away from each other).

For example:

Two ships are approaching Earth from opposite directions. As seen from earth, they are at exactly the same distance, each traveling at 0.5c, and will of course arrive simultaneously. One minute before their arrival, Earth sends out a signal to sync the clocks of the ships. The ships are at that moment 30 light seconds away, and light travels towards them at a relative speed (seen by earth) of 1.5c (light going one way at c, ship going the other way at 0.5c), so it will take 20 seconds for the signal to arrive at both ships, which are at that time 20 light seconds away. Both start their timers, and on arrival both clocks show 34.64 seconds have passed (instead of 40 as measured by earth). This is of course because both clocks are only running at 87% of their normal speed.

Now, imagine we are on board of one of the ships.

We can consider ourselves to be stationary, while the Earth is moving towards us with a speed of 0.5c, and the other ship is approaching us with 0.8c (relativistic addition of 0.5+0.5). This means that the other ship has a speed relative to Earth of only 0.3c. Since we arrived at the same time, this means the distance between Earth and the other ship must have been 60% of the distance between us and the Earth at any given "simultaneous" time before arrival.

We received the signal 34.64 seconds before arrival, when Earth was 17.32 light seconds away. Earth would measure that as 20 light seconds because of length contraction (87%). Since Earth is moving towards us at 0.5c, the message must have been sent when Earth was twice as far away, at 34.64 light seconds from us. So the message was sent 69.28 seconds before our arrival (but Earth will have measured that as only one minute because their clocks are slower at a rate of 87%).

When Earth sent the message, the other ship was 20.78 light seconds away from Earth (69.28 times 0.3). Since the message travels at a speed of 1.8c relative to the other ship (light going one way at c, ship going the other way at 0.8c), it was received after 11.55 seconds, which is 57.73 seconds before arrival, when they were... 17.32 light seconds from Earth (57.63*0.3). At least we agree we received the signal at the same distance from earth! They just got to that distance a lot earlier than us, and took longer to reach Earth from there, but of course they would measure those 57.73 seconds as only 34.64 seconds because their clock is ticking at 60% of normal speed. That explains why their clock is indicating exactly the same elapsed time as ours.

Getting dizzy yet? ;-)